The Dirichlet Process (DP) is indexed by a concentration parameter \(\alpha \)  and
a base distribution \(G_0\) , denoted \(DP(G_0, \alpha )\) . It has a long history of
being used as a clustering prior for a set of points, \(\lbrace x_1, \dots x_N\rbrace \) , and
was first investigated by [1]} and [2]}. More
recently, computationally efficient methods have been developed for parameter
estimation by [3]}, [4]}, and
[5]}. Using a stick breaking construction of the Dirichlet
process, it can be shown that \(G(x) = \sum _{k = 1}^\infty \pi _k\delta _{\theta _k}(x)\)  is a sample from a \(DP(G_0, \alpha )\) , where \(\pi _k = V_k\prod _{l = 1}^{k - 1} (1 - V_l)\) , \(V_k \overset{iid}{\sim }\text{Beta}(1, \alpha )\) , and
\(\theta _k \overset{iid}{\sim }G_0\)  [6]}. Hence, the
distributions sampled from a Dirichlet Process are a countably infinite mixture
of point masses.
